I had tennis elbow in right elbow for which I received cortizone injections. I eventually needed surgery.
I also had ulnar nerve surgery due to repeated dislocation of the ulnar nerve. The symptoms of which were pain on bending and straightening of the elbow and tingling down the outer side of my hand. Surgery resolved both problems.
I doubt your problem would be due to arthritis but you may need the advice of a doctor. Ice pack, rest from lifting and anti-inflammatory medication may work for you. Good luck.